Miles Wheeler - Nonexistence of subcritical solitary waves

We prove that all solitary gravity waves are supercritical, i.e. they travel faster than infinitesimal periodic waves. Previously, this basic fact was only known under additional sign conditions or smallness assumptions. While there are physical grounds for expecting subcritical solitary waves to be extremely rare, it seems impossible to turn these ideas into a rigorous proof. Instead, our argument hinges on a new function which is related to the flow force and has several surprising properties.

This is joint work with Vladimir Kozlov and Evgeniy Lokharu